Send a Ctrl+a with "Ctrl+a a"
Send a Ctrl+a with "Ctrl+a a"

You had bound "Ctrl+a Ctrl+a" twice: once in line 7 for send-prefix and then you redefine it in line 15 to cycle panes.  Leave the pane cycling to "Ctrl+a Ctrl+a" and let "Ctrl+a a" send a "Ctrl+a" to the underlying command.
derkling/dotfiles,derkling/dotfiles,derkling/dotfiles,derkling/dotfiles